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Proof step 20 from proof range-extend (previous step)

range=(copy(ar, n, ar0, n0 + m0, m1), n0, ar1, n1, m0), range=(copy(ar, n, ar0, n0 + m0, m1), n0 + m0, ar1, n1 + m0, m1), n0 + m0 + m1 ≤ # ar0, n + m1 ≤ # ar ⊦ (n1 + m0) + m1 ≤ # ar1 ∧ (n2 < m1 → ar[n + n2] = ar1[(n1 + m0) + n2])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 21:
⊦ range=(ar0, n0, ar1, n1, m) ↔ n0 + m ≤ # ar0 ∧ n1 + m ≤ # ar1 ∧ (∀ n. n < m → ar0[n0 + n] = ar1[n1 + n])
Proof step 22:
range=(copy(ar, n, ar0, n0 + m0, m1), n0, ar1, n1, m0), n + m1 ≤ # ar, n0 + m0 + m1 ≤ # ar0, (n0 + m0) + m1 ≤ # copy(ar, n, ar0, n0 + m0, m1), (n1 + m0) + m1 ≤ # ar1, ∀ n2. n2 < m1 → copy(ar, n, ar0, n0 + m0, m1)[(n0 + m0) + n2] = ar1[(n1 + m0) + n2] ⊦ (n1 + m0) + m1 ≤ # ar1 ∧ (n2 < m1 → ar[n + n2] = ar1[(n1 + m0) + n2])

Rule argument

spec: <toplevel> name: range-eq-ext seq: ⊦ range=(ar0, n0, ar1, n1, m) ↔ n0 + m ≤ # ar0 ∧ n1 + m ≤ # ar1 ∧ (∀ n. n < m → ar0[n0 + n] = ar1[n1 + n]) subst: [m, n1, ar1, n0, ar0] → [m1, n1 + m0, ar1, n0 + m0, copy(ar, n, ar0, n0 + m0, m1)] flags: <all paths>

Additional information

Used terms: m1, n1 + m0, ar1, n0 + m0, copy(ar, n, ar0, n0 + m0, m1)